# Rare event modeling with self-regularized normalizing flows: what can we learn from a single failure?

arXiv: https://arxiv.org/abs/2502.21110 · HTML: https://mlsanity.com/paper/2502.21110/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 54 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Builds on (most cited first, 30 of 31)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [CFLOW-AD: Real-Time Unsupervised Anomaly Detection with Localization via Conditional Normalizing Flows](https://mlsanity.com/paper/2107.12571/) (2021)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [Same Same But DifferNet: Semi-Supervised Defect Detection with Normalizing Flows](https://mlsanity.com/paper/2008.12577/) (2020)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Few-shot Image Generation via Cross-domain Correspondence](https://mlsanity.com/paper/2104.06820/) (2021)
- [Guided Conditional Diffusion for Controllable Traffic Simulation](https://mlsanity.com/paper/2210.17366/) (2022)
- [OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transport](https://mlsanity.com/paper/2006.00104/) (2020)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)
- [Scalable End-to-End Autonomous Vehicle Testing via Rare-event Simulation](https://mlsanity.com/paper/1811.00145/) (2018)
- [A Survey of Algorithms for Black-Box Safety Validation of Cyber-Physical Systems](https://mlsanity.com/paper/2005.02979/) (2020)
- [A Bayesian Data Augmentation Approach for Learning Deep Models](https://mlsanity.com/paper/1710.10564/) (2017)
- [OpenFWI: Large-Scale Multi-Structural Benchmark Datasets for Seismic Full Waveform Inversion](https://mlsanity.com/paper/2111.02926/) (2021)
- [Neural Bridge Sampling for Evaluating Safety-Critical Autonomous Systems](https://mlsanity.com/paper/2008.10581/) (2020)
- [Toward Understanding Generative Data Augmentation](https://mlsanity.com/paper/2305.17476/) (2023)
- [A Survey on Generative Modeling with Limited Data, Few Shots, and Zero Shot](https://mlsanity.com/paper/2307.14397/) (2023)
- [On the expressivity of bi-Lipschitz normalizing flows](https://mlsanity.com/paper/2107.07232/) (2021)
- [Few-shot Image Generation with Mixup-based Distance Learning](https://mlsanity.com/paper/2111.11672/) (2021)
- [ALFA: A Dataset for UAV Fault and Anomaly Detection](https://mlsanity.com/paper/1907.06268/) (2019)
- [Optimization for Amortized Inverse Problems](https://mlsanity.com/paper/2210.13983/) (2022)
- [Model-based Validation as Probabilistic Inference](https://mlsanity.com/paper/2305.09930/) (2023)

## Built on by (most cited first, 1 of 1)

- [Repulsive normalizing flow mixtures for adaptive importance sampling: reliability analysis of complex systems](https://mlsanity.com/paper/2609.21160/) (2026)

## Abstract (arXiv)

Increased deployment of autonomous systems in fields like transportation and robotics have seen a corresponding increase in safety-critical failures. These failures can be difficult to model and debug due to the relative lack of data: compared to tens of thousands of examples from normal operations, we may have only seconds of data leading up to the failure. This scarcity makes it challenging to train generative models of rare failure events, as existing methods risk either overfitting to noise in the limited failure dataset or underfitting due to an overly strong prior. We address this challenge with CalNF, or calibrated normalizing flows, a self-regularized framework for posterior learning from limited data. CalNF achieves state-of-the-art performance on data-limited failure modeling and inverse problems and enables a first-of-a-kind case study into the root causes of the 2022 Southwest Airlines scheduling crisis.